In an assembly, magnetic nanoparticles primarily interact because of dipolar interaction. The energy associated with such interaction can be evaluated using the following expression [1]}, [2]}
\(E^{}_{\mathrm {dip}}=\frac{\mu ^{}_o\mu ^2}{4\pi a^3}\sum _{j,\ j\ne i}\left[ \frac{\hat{\mu _{i}}\cdot \hat{\mu _{j}}-3\left(\hat{\mu _{i}}\cdot \hat{r}_{ij}\right)\left(\hat{\mu _{j}}\cdot \hat{r}_{ij}\right)}{(r^{}_{ij}/a)^3}\right].\) 
